Michigan Mathematical Journal
- Michigan Math. J.
- Volume 69, Issue 1 (2020), 179-200.
Absolutely Convergent Fourier Series of Functions over Homogeneous Spaces of Compact Groups
This paper presents a systematic study for classical aspects of functions with absolutely convergent Fourier series over homogeneous spaces of compact groups. Let be a compact group, be a closed subgroup of , and be the normalized -invariant measure over the left coset space associated with Weil’s formula with respect to the probability measures of and . We introduce the abstract notion of functions with absolutely convergent Fourier series in the Banach function space . We then present some analytic characterizations for the linear space consisting of functions with absolutely convergent Fourier series over the compact homogeneous space .
Michigan Math. J., Volume 69, Issue 1 (2020), 179-200.
Received: 20 February 2018
Revised: 24 April 2018
First available in Project Euclid: 21 November 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20G05: Representation theory 43A85: Analysis on homogeneous spaces
Secondary: 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. 43A90: Spherical functions [See also 22E45, 22E46, 33C55]
Ghaani Farashahi, Arash. Absolutely Convergent Fourier Series of Functions over Homogeneous Spaces of Compact Groups. Michigan Math. J. 69 (2020), no. 1, 179--200. doi:10.1307/mmj/1574326881. https://projecteuclid.org/euclid.mmj/1574326881